调研、论文、教育、考证学习（4421 个）
Find numerical solutions where a function equals zero. The skill helps choose a method based on known intervals and available derivatives, then guides SciPy implementation, searches for multiple solutions, and checks accuracy and valid ranges.
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Helps select graph algorithms for shortest paths, minimum spanning trees, network flow, and coloring. Provides decision guides and example commands for symbolic calculations and checking mathematical properties.
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Build understanding of mathematical ideas before calculating. The skill guides you through concrete examples, diagrams, simpler cases, and analogies, then summarizes the intuition and suggests a next step with a check.
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Work through first-order ordinary differential equations by classifying their form and choosing a solution method. The skill also covers numerical initial-value problems, checking solutions against the equation and conditions, and examining equilibrium stability.
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Plan and examine proofs in mathematical logic. Choose direct proof, contradiction, cases, or induction, then review proof structure using concepts such as cut elimination, soundness, and completeness, with command examples for checking proof steps.
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Analyze propositional formulas and arguments using truth tables, deduction rules, and branching proof trees. Classify formulas as always true, always false, or dependent on their inputs, and check whether an argument follows from its premises.
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Work through continuity problems in real analysis by checking function values and limits. The skill outlines separate checks for piecewise functions and provides commands for limit calculations with SymPy and proof checks with Z3.
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Work through abstract algebra problems about rings by checking their defining rules and properties. The skill organizes questions about ideals and structure-preserving maps, with Z3 and Sympy command examples for proof checks and symbolic calculations.
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Study source coding, the information theory behind data compression. The skill guides problems involving Huffman codes, average code length, prefix-code constraints, arithmetic coding, and the tradeoff between compression rate and distortion, with calculation and proof command examples.
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Turn mathematical claims into Lean4 proofs, checked by a theorem prover. A five-phase workflow researches existing results, designs the proof, tests candidate lemmas, implements it, and reports remaining proof gaps and any custom axioms.
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Research library usage, recommended approaches, and general topics using external documentation and web sources. Choose a brief or thorough investigation, then organize examples, pitfalls, comparisons, and source links into a research document or implementation handoff.
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Researches library documentation, implementation practices, and specific web pages using Nia, Perplexity, and Firecrawl through MCP tools. Produces a handoff document with findings, available code examples, recommendations, pitfalls, and source links for another agent.
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Use Pint to convert measurements, calculate with units, and check whether units describe compatible physical quantities. It also breaks quantities into values and units, simplifies compound units, and returns calculation results as JSON.
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Use Perplexity to find web sources, get cited research summaries, explore complex decisions, or investigate a topic in depth. Separate modes support quick questions, ranked search results, combined answers, and comprehensive research.
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Find the right tool for equations, calculus, numerical calculations, proof checks, or math practice. The guide connects tasks to commands for computing results, verifying steps, requesting hints, and plotting functions.
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Turn math requests into specific command-line instructions using pattern-based routing. It covers calculus, equations, unit conversion, geometry, logical proofs, and plotting, returning a command for the agent to execute with the corresponding math script.
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Handle equations, calculus, matrices, unit conversions, and mathematical explanations through one entry point. The skill selects a suitable calculation tool or topic guide, including symbolic math tools that work directly with expressions.
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Retrieve web page content from a URL or search query through Firecrawl MCP. Export it as Markdown, HTML, or plain text, with support for extracting structured data from pages.
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Investigate where or when a photo was taken using visible clues, metadata, reverse image search, maps, and image comparisons. Results include coordinates, an error radius, evidence images, and confidence levels that distinguish verified findings from uncertain candidates.
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Search Wayback Machine archives for deleted GitHub files, issues, pull requests, and wiki pages. Recover available text and repository details from saved web pages to investigate a project's past state.
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Prepares Claude Code or OpenAI Codex for in-depth research with hyperresearch, then hands the request to a structured workflow for research reports, literature reviews, and analysis using multiple sources with verified citations.
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Investigate firsthand sources before making a judgment or recommendation. Separate verified facts, reasoned inferences, and unknowns, document their sources, and produce a conclusion that explains the current situation, constraints, and remaining uncertainty.
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Investigate a topic with cooperating agents assigned to distinct questions. Track sources, conflicting evidence, and unresolved claims, then assemble a cited deliverable with verification records and quality checks suited to the requested format.
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Retrieve pages blocked by web access filters, read Chinese and social platforms through dedicated tools, and inspect archived copies with their dates. Escalate to browser interaction when simpler extraction methods cannot provide the needed content.
中文简介正在准备中。当前显示英语简介。